During the past two decades, there has been an increasing interest in the development of thermoacoustic cooling engines (pumps) for a variety of commercial, military and industrial applications. Interest in thermoacoustic cooling has accelerated rapidly with the production ban of chlorofluorocarbons (CFC's). Thermoacoustic refrigerators can be constructed such that they use only inert gases, which are non-toxic and do not contribute to ozone depletion, nor to global warming. Exemplary prior art designs for thermoacoustic engines and refrigerators are shown in the following patents: U.S. Pat. Nos. 4,489,553, 4,722,201, 5,303,555, 5,647,216, 5,953,921, 6,032,464, and 6,314,740.
Most of the thermoacoustic engines and refrigerators that consume or produce electrical power require the containment of the thermoacoustic components and the gaseous working fluid within a rigid-walled enclosure (pressure vessel). The pressure vessel is typically either a rigid-walled adiabatic compression volume or a rigid-walled acoustic resonator of either the standing-wave or Helmholtz type. Within these rigid enclosures, oscillatory pressures are produced. If one is building an electrically-driven thermoacoustic refrigerator, there is usually a piston that is actuated by some electro-mechanical transducer (e.g., loudspeaker or other motor mechanism) contained within, or attached to the rigid enclosure. Motion of that piston produces the required pressure oscillations. The piston is coupled to the rigid enclosure, containing the thermoacoustic components, by some means that provides a dynamic pressure seal against leakage of the gaseous working fluid around the piston. In all known cases except one, this dynamic pressure seal is either a clearance seal (e.g., a close-fitting surface that surrounds the piston) or a flexure seal, such as a bellows or diaphragm. The only exception is the Torsionally-Resonant Toroidal Thermoacoustic Refrigerator (T-RTTAR) (see U.S. Pat. No. 5,953,921). The T-RTTAR approach does not employ a dynamic pressure seal, but requires that the entire rigid enclosure be oscillated at the operating frequency.
In a thermoacoustic prime mover (engine), the pressure oscillations are generated thermoacoustically when thermal energy (heat) is supplied to the engine. To extract electrical power from such thermoacoustically-induced pressure oscillations within the rigid enclosure, a piston, which is connected to an electro-mechanical transducer, is driven by the pressure oscillations. Again, a dynamic pressure seal is required to suppress the flow of the gaseous working fluid around the piston.
Adiabatic Compression Volume
The simplest implementation of a rigid enclosure used to contain the thermoacoustic components and the gaseous working fluid for a thermoacoustic device is one for which each of the rigid enclosure's dimensions is small compared to the acoustic wavelength. An example of such a device is shown in FIG. 1, which is taken from U.S. Pat. No. 6,314,740 to DeBlok (originally FIG. 2). The acoustic wavelength, λ, is given by the formula λ=a/f, where the sound speed in the gas or gas mixture within the resonator is a, and piston oscillation frequency is f. One or more pistons, oscillating sinusoidally at frequency f, use electrical power to produce the pressure oscillations or utilize those pressure oscillations to produce electrical power. The relationship between the pressure oscillations and the enclosure volume changes caused by the motion of the piston is controlled by the adiabatic gas law if the smallest dimension of the rigid enclosure, Ltyp (usually the length or diameter of the rigid enclosure), is small compared to the acoustic wavelength, Ltyp<<λ. For higher power thermoacoustic devices, the wavelength, λ, is typically on the order of one meter.
Another consideration in the design of thermoacoustic devices is the thermal penetration depth, δκ, which serves as a characteristic length that describes over what distance heat can diffuse through the working fluid during an acoustic cycle. The rigid enclosure's smallest dimension is always large compared to the thermal penetration depth, δκ. That is, Ltyp>>δκ. In most thermoacoustic applications, the thermal penetration depth, δκ, is typically on the order of 100 micrometers (100 μm).
                              δ          κ                =                              κ                          π              ⁢                                                          ⁢              ρ              ⁢                                                          ⁢                              c                p                            ⁢              f                                                          (        1        )            The thermal penetration depth depends upon the density ρ, thermal conductivity κ, and isobaric specific heat cp of the gaseous working fluid, as well as on the frequency of operation f.
Where the acoustic wavelength is large compared to the rigid enclosure's dimensions, the pressure oscillations everywhere within the enclosure are to a very good approximation constant (i.e. p1(t)=p1 sin (2πft) regardless of position), and to the extent that the volume of gas within the enclosure is large compared to the product of the interior surface area and the thermal penetration depth, the pressure oscillations are to a good approximation governed by the adiabatic gas law, pVγ=constant. The polytropic coefficient of the gaseous working fluid, γ, is the ratio of the specific heat of the gas at constant pressure, cp, to the specific heat of the gas at constant volume, cv.
  γ  =            c      p              c      v      
For small changes in the rigid enclosure volume, Vo, that contains the gaseous working fluid at the mean (static) pressure, pm, the magnitude of the oscillatory pressure, p1, can be expressed in terms of the magnitude of the change in the volume of the rigid enclosure, δV, using the adiabatic gas law.
                              p          1                =                  γ          ⁢                                          ⁢                      p            m                    ⁢                                    δ              ⁢                                                          ⁢              V                                      V              o                                                          (        3        )            
The motion of the piston produces the change in the volume of the rigid enclosure. The magnitude of the oscillatory pressure, p1, can be related to the magnitude of the piston motion, yo, using the area of the piston, Apist. The time-dependent, sinusoidal displacement of the piston is given by ypist (t)=y1 sin (2πft), which has a displacement amplitude, y1. The internal volume of the rigid enclosure is Vo, if it is measured when the piston is at its neutral or equilibrium position, ypist=0. At the neutral piston position the gas pressure within the rigid enclosure is equal to the mean pressure pm,
                              p          1                =                                            γ              ⁢                                                          ⁢                              p                m                            ⁢                              A                pist                                                    V              o                                ⁢                                    y              1                        .                                              (        4        )            
The above result (Equation 4) demonstrates that for a given volume defined by the rigid enclosure volume, Vo, and piston area, Apist, the magnitude of the pressure oscillations, p1, is increased as the magnitude of the piston displacement, y1, is increased. To simplify comparison of the performance of an adiabatic compression volume to the performance of a standing-wave resonator, it is convenient to characterize the piston's motion by expressing its motion as producing an oscillatory volume flow rate of amplitude dV/dt=2πfy1Apist. The result of (Equation 4) can then be expressed as an acoustic impedance Zac=p1/(dV/dt),
                                          Z                          a              ⁢                                                          ⁢              c                                ≡                                    p              1                                      (                              dV                /                dt                            )                                      =                                            γ              ⁢                                                          ⁢                              p                m                                                    2              ⁢              π              ⁢                                                          ⁢              f              ⁢                                                          ⁢                              V                o                                              .                                    (        5        )            
FIG. 1 illustrates an earlier design that uses this adiabatic compression volume approach. As shown, a piston is joined to a rigid enclosure by a flexible bellows. An electromechanical actuator 2 is attached to the piston-bellows combination 3, which is joined to the rigid enclosure 1 that contains the thermoacoustic elements of this refrigeration system. An acoustic phase control bypass 10 is formed by an internal connection tube 12. A cold heat exchanger is shown at 6, with cold transport fluid inlet 6a and outlet 6b provided for connection to a refrigeration load. A hot heat exchanger is shown at 7, with hot transport fluid inlet 7a and outlet 7b providing a means to exhaust the waste heat that is pumped by the regenerator 8.
For the device of FIG. 1, the volume of the bellows, Vbel, constitutes a very small fraction of the total volume, Vo, of the rigid enclosure that contains the gaseous working fluid and the thermoacoustic components. Since the motion of the bellows, and hence the motion of the piston, y1, is limited by displacement and pressure induced stresses in the bellows material (typically metal), the pressure oscillation magnitude, p1, given by Equation 4, will be smaller than desirable for high cooling power density in the refrigeration application contemplated by the inventor.
Bellows Excursion (Stroke) Limitations
The limitations placed on pressure oscillation magnitude by the design of the device of FIG. 1 are not unique to that design. Instead, this is a serious problem faced by a range of thermoacoustic devices. Additionally, the bellows themselves place certain limitations on devices which make use of them. The useful lifetime of a bellows (number of cycles-to-failure, Nmax) is determined by the magnitude of the combined static and dynamic stresses produced in the bellows material due to the bellows excursions in compression and extension and the pressure differential across the bellows. The sum of these excursion and pressure induced stresses must be compared to the endurance limit (the maximum material stress allowable for an infinite number of cycles-to-failure Nmax=∞) of the bellows material. Expressions for calculation of these stresses and the expected number of cycles-to-failure for bellows are provided in the Standards of the Expansion Joint Manufacturer's Association, Inc., 25 North Broadway, Tarrytown, N.Y. 10591 (EJMA Standards).
The EJMA Standards also provide expressions for calculation of the frequencies, fbel, for the compressional standing-wave resonance of a bellows of a given length, Lbel. It has been shown by R. W. M. Smith [High Efficiency Two Kilowatt Acoustic Source for a Thernoacoustic Refrigerator, Penn State Applied Research Laboratory Technical Report No. TR 01-001 (November 2000), pages 43–45] that for dynamic flexure of bellows at frequencies greater than about fbel/20, the EJMA Standards have to be supplemented by a dynamic stress concentration factor.
To appreciate the limitation imposed by the change in volume, δV, dictated by the bellows excursion amplitude restrictions discussed above, it is useful to partition the enclosure volume, Vo, into a static portion defined by the rigid enclosure, Venc, and the volume of the bellows, Vbel. Therefore, Vo=Venc+Vbel. The restrictions on volume change, δV, for a bellows imposed by the EJMA Standards and Smith's dynamic stress concentration factor tends to limit volume change, δV, to about 10% of the bellows volume, Vbel, so that δV≦0.10 Vbel. Equivalently, for a rigid enclosure and bellows of constant cross-sectional area, y1/Lbel≦10%. Inspection of FIG. 1 suggests that for De Blok's configuration, the bellows volume is less than 20% of the total volume, Vbel<0.20 Vo. Consequently, in the De Blok configuration, δV/Vo<0.02. This small compression ratio, δV/Vo, suggests that the peak-to-mean pressure ratio, p1/pm=γδV/Vo, for such a device is also on the order of only a few percent (≦3%).
Most thermoacoustic devices require that the peak-to-mean pressure ratio, p1/pm be greater than 3% to be of practical value. Peak-to-mean pressure ratios in the range of 5%<p1/pm<10% have most commonly been used to date to produce the optimum ratio of cooling power volumetric density (for a thermoacoustic refrigerator) to non-linear dissipation produced by high gaseous working fluid flows, although higher pressure amplitudes are expected to be attractive, when such losses can be reduced. For thermoacoustic prime movers (engines), the preferred peak-to-mean pressure ratios, p1/pm, have tended to even larger values than those consider by most designers to be optimal for refrigeration applications.
The small compression ratios characteristic of the De Blok configuration in FIG. 1 can be overcome by using a thermoacoustic engine to produce the oscillatory pressure required by the thermoacoustic refrigerator [see, for example, U.S. Pat. Nos. 4,858,441; 5,901,556; 6,032,464 or Reh-lin Chen, “Design, construction and measurement of a large solar powered thermoacoustic cooler,” Penn State (December 2001)] if the refrigeration application is better suited being driven by thermal, rather than electrical power. However, many applications are better suited to the use of electrical power.
Clearance Seal Limitations
The limitations of the small compression ratio of the bellows can also be overcome if a clearance seal is used instead of a bellows (flexure) seal to suppress flow of the gaseous working fluid around the piston. Use of the clearance seal approach introduces additional power dissipation due to fluid friction in the small gap between the piston and the bore, as well as “blow-by” losses due to gas flow through the gap. Use of the clearance seal approach also produces de-centering of the piston's motion (known as “piston walking”) that will move the equilibrium position of the piston and linear motor. This piston walking is due to the build-up of a static pressure differential which can be produced by the asymmetry of the pressure in the compression and expansion strokes or the synchronous “gap wobble” of the piston within its bore [see G. W. Swift, Thermoacoustics: A unifying perspective for some engines and refrigerators (Acoustical Society of America, 2002)]. That differential pressure has to be relieved with a relief valve or other means, such as an acoustical bypass network as taught by W. C. Ward, J. C. Corey, and G. W. Swift, [see “Drift stabilizer for reciprocating free-piston devices,” filed April 2001, Los Alamos National Laboratory, Case S-94,784].
Acoustic Resonator
Most of the thermoacoustic engines and refrigerators that produce (for engines) or consume (for refrigerators and heat pumps) electrical power make use of the placement of the thermoacoustic components, and the gaseous working fluid, within a rigid-walled enclosure that operates as a standing-wave or Helmholtz (lumped parameter) acoustical resonator. For the purposes of this discussion, both the “standing-wave” and the “Helmholtz” resonators are considered to be rigid-walled enclosures that use the inertial and elastic properties of the gaseous working fluid to create an acoustical resonance within the enclosure. Acoustical resonance of the gaseous working fluid enhances the amplitude of the pressure oscillations for a given piston motion (typically characterized by the volume velocity, dV/dt, induced by the piston's oscillations) over the amplitude of an adiabatic compression volume by a factor of Q/π, if the volume of the two rigid enclosures are equal. This may produce a desirable effect, since increased pressure amplitude or reduced piston motion generally improve performance (power density) and/or increase reliability.
The use of a cavity that is an acoustic resonator provides a means of increasing the pressure oscillations of the gaseous working fluid over the pressure oscillations that would be possible for the same amplitude of the piston motion at some frequency that is not a resonance of the rigid cavity (see S. Garrett and S. Backhaus, “The Power of Sound,” American Scientist Magazine 88(6), 516–525 (2000)]. This resonant pressure enhancement will be dependent upon the geometrical shape of the resonator. If we consider a standing-wave resonator that is operated in a mode that contains one half-wavelength, λ/2, in the longer dimension, and has a quality factor Q, then the acoustic impedance, Zac, of the resonator is given [see I. Rudnick, Journal of the Acoustical Society of America 63(6), 1923–1925 (1978)] by,
                                          Z                          a              ⁢                                                          ⁢              c                                ≡                                    p              1                                      (                              dV                /                dt                            )                                      =                              γ            ⁢                                                  ⁢                          p              m                        ⁢            Q                                π            ⁢                                                  ⁢            f            ⁢                                                  ⁢                          V              o                                                          (        6        )            
Comparison of the result for the acoustical impedance, Zac, of the half-wavelength, λ/2, standing-wave resonator (Equation 6), with the impedance of the adiabatic compression volume (Equation 5), shows that for rigid enclosures of the same volume, Vo, the standing-wave resonator produces Q/2 times greater pressure, p1, for the same oscillatory piston volume flow rate, dV/dt. This oscillating pressure enhancement can be substantial, since thermoacoustic resonators typically have a large quality factor, such as Q≅20±10. As taught by Wakeland [see J. Acoust. Soc. Am. 107(2), 827–832 (2000)], limitations imposed by the stroke of the linear motor and the mechanical impedance that produces the maximum electro-acoustic energy conversion efficiency for that motor, may not make the acoustic resonant Q-enhancement of Equation 6 useful unless there is sufficient latitude in the choice of piston area, Apist, for a given application and choice of linear motor.
The oscillatory pressure increase created by the acoustical resonator, as well as the increased surface area of such a resonator compared to an equivalent adiabatic compression volume, can also introduce additional dissipation. This resonator dissipation is due primarily to the high velocities of the gaseous working fluid near the center of a standing-wave resonator or in the neck of a Helmholtz resonator at high amplitudes and due to thermoviscous boundary layer losses at lower amplitudes. Rigid enclosures that function as acoustical resonators also tend to be significantly longer than adiabatic compression volumes for containment of thermoacoustic components rated for the same cooling or power generation capacities.
In light of the above, there is a need for improved thermoacoustic devices, which overcome the shortcomings of the prior art.